Solve for $x$ and $y$ using elimination. $\begin{align*}-3x-5y &= -2 \\ x-9y &= -6\end{align*}$
We can eliminate $x$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $1$ and the bottom equation by $3$ $\begin{align*}-3x-5y &= -2\\ 3x-27y &= -18\end{align*}$ Add the top and bottom equations. $-32y = -20$ Divide both sides by $-32$ and reduce as necessary. $y = \dfrac{5}{8}$ Substitute $\dfrac{5}{8}$ for $y$ in the top equation. $-3x-5( \dfrac{5}{8}) = -2$ $-3x-\dfrac{25}{8} = -2$ $-3x = \dfrac{9}{8}$ $x = -\dfrac{3}{8}$ The solution is $\enspace x = -\dfrac{3}{8}, \enspace y = \dfrac{5}{8}$.